Improved Inference of Soil Behaviour and Model Parameters In Geotechnics Using Bayesian Methods

Statistical techniques are of major interest at present in geotechnics, especially where parameters are sought, using field or lab tests, or numerical simulations. Bayesian inference (BI) methods provide improved distributions of parameter values based on instances of observed data (so-called ensembles, e.g. lab tests or numerical simulations) however in geotechnical problems, the prior information obtained from the ensemble forecast usually suffers from errors due to “covariance insufficiency”. This paper addresses this issue and presents a new method to reduce these errors. This is achieved by perturbing the boundary conditions in the generation of ensembles with “augmented prior error covariance”, and by inflating the covariance through the “relaxation to prior” method. To prove the effectiveness of the approach, we demonstrate a Finite Element-BI (FE-BI) system, comprising an in-house FE code for ensemble forecast, an observation operator to link the forecast results to the observed data, and a Bayesian inference module, in which an ensemble Kalman filter is applied. The FE-BI system introduces a number of novel features: (1) the ensemble forecast is improved through the proposed error covariance inflation approach; (2) both the soil behaviours and model parameters are inferred simultaneously; and (3) computational cost is significantly reduced compared with batch calibration processes. Three illustrative examples are presented to demonstrate the applicability of the FE-BI system: an undrained compression triaxial test with the modified Cam Clay model; cyclic triaxial tests with the small strain overlay (SSO) model of Benz et al. (2009); and simulation of a braced excavation with a Drucker-Prager SSO model. Results show that the FE-BI system can effectively infer the soil behaviours based on the observed data, by narrowing the posterior distribution for each parameter which leads to model parameters with high certainty.